Determination of the Young modulus (PAG 2)
Determine the Young modulus of a metal wire by loading it and measuring extension.
Apparatus
- Long metal wire (~2 m) clamped from above
- Micrometer screw gauge
- Metre rule and vernier scale
- Slotted masses and hanger
- Reference wire (same material, same clamp point)
Safety
- Wear goggles in case the wire snaps.
- Use a tray below the hanging masses.
Method
- Clamp both the reference wire and test wire from the same overhead support.
- Measure unstretched length L and diameter d (micrometer, three positions).
- Add masses to the test wire in 100 g increments; read extension x from vernier scale after each addition.
- Unload and confirm elastic recovery.
- Plot stress $\sigma = F/A$ vs strain $\varepsilon = x/L$; gradient $= E$.
Key Variables
Independent
Applied force F
Dependent
Extension x
Controlled
Temperature; Length L; Cross-section A
Analysis and Results
- $E = \sigma/\varepsilon = FL/(Ax)$.
- Gradient of stress-strain graph $= E$.
- Reference wire eliminates errors from support sag and thermal expansion.
Common Errors
- Overloading the wire beyond its elastic limit.
- Measuring diameter at only one point.
- Not zeroing the vernier before the first mass is added.
Exam-style questions on this practical. Click Show mark scheme to reveal the answer after attempting each question.
Q14 marks
A steel wire (length 2.0 m, diameter 0.50 mm) extends by $1.4$ mm under a 20 N load. Calculate the Young modulus.
Q22 marks
Why is a reference wire used alongside the test wire?